A hospital therapeutics committee is evaluating a recent study on a novel biologic agent f… — USMLE Step 3

A hospital therapeutics committee is evaluating a recent study on a novel biologic agent for severe uncontrolled asthma to decide on formulary inclusion. The study's baseline characteristics table summarizes the participants' prior healthcare utilization. Specifically, the number of emergency department visits per patient over the $12$ months prior to enrollment is reported with a mean of $1.5$ and a standard deviation of $2.8$ . The committee notes that the lowest possible number of emergency department visits is $0$ . Which of the following best explains why the authors' method of summarizing this specific baseline data is methodologically flawed?

The distribution is right-skewed, so the median and interquartile range should be used to describe the central tendency and dispersion.Answer
B
The number of visits is an ordinal variable, meaning that calculating a mean is mathematically invalid and only the mode should be reported.
C
The standard deviation exceeds the mean, which indicates a left-skewed distribution where most values are clustered above the mean.
D
The data represents a continuous variable, which requires reporting the 95% confidence interval rather than a standard deviation for accurate interpretation.
E
The wide standard deviation suggests a high prevalence of effect modification, which confounds the baseline descriptive statistics.

Answer

The distribution is right-skewed, so the median and interquartile range should be used to describe the central tendency and dispersion.

The correct answer accurately identifies that the data is heavily right-skewed. The variable is a count (discrete data) with a hard lower limit of

0

. A mean of

1.5

with a standard deviation of

2.8

indicates that if the distribution were symmetrical, a large proportion of patients would have a negative number of visits, which is impossible. Therefore, the data must be bunched near

0

with a long tail extending to the right (a positive, or right, skew) caused by a few outlier patients with numerous visits. Because the mean is heavily influenced by these high-end outliers, it does not represent the 'typical' patient well. In such skewed distributions, non-parametric descriptive statistics—specifically the median (for central tendency) and the interquartile range (for dispersion)—provide a much more accurate summary of the cohort.

Step-by-Step Solution

Identify the data type and its boundaries.

The 'number of emergency department visits' is a discrete quantitative variable (count data) that has an absolute minimum boundary of

0

Understanding the limits of the data is required to conceptualize its distribution shape.

Apply the properties of the mean and standard deviation to the given data.

The mean is

1.5

and the standard deviation is

2.8

. If the data were normally distributed (symmetrical), approximately

16\%

of the values would fall below one standard deviation under the mean (

1.5 - 2.8 = -1.3

Checking if a normal distribution is physically possible for the dataset reveals the underlying distribution shape.

Determine the true shape of the distribution and select the appropriate statistical measures.

Since negative visits are impossible, the data cannot be symmetrical. The large standard deviation is driven by a small number of patients with a very high number of visits, creating a long right tail (positive skew). For heavily skewed data, the median and interquartile range are the most accurate descriptors.

The mean is highly sensitive to outliers in the tail, making it artificially high and unrepresentative of the typical patient.

Key Concept

When continuous or discrete data is highly skewed (e.g., when bounded at zero with a standard deviation larger than the mean), the mean and standard deviation are misleading, and the median and interquartile range (IQR) should be used.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic